This problem asks you to analyze the IS-LM model algebraically. Suppose consumptionis a linear function of disposable income:C(YT) = a + b(YT)where a > 0 and 0 < b < 1. Suppose also that investment is a linear function of theinterest rate:I(r) = c — drwhere c> 0 and d > 0.(a) Solve for Y as a function of r, the exogenous variables G and T, and the model'sparameters a, b, c, and d.(b) How does the slope of the IS curve depend on the parameter d, the interest ratesensitivity of investment? Refer to your answer to part (a), and explain the intu-ition.(c) Which will cause a bigger horizontal shift in the IS curve, a $100 tax cut or a $100increase in government spending? Refer to your answer to part (a), and explainthe intuition.

Given information: Linear function, C(Y - T) = a + b (Y - T) Investment linear function, I (r) = c -…

This problem asks you to analyze the IS-LM model algebraically. Suppose consumption is a linear function of disposable income: C(YT) = a + b(Y − T) where a > 0 and 0 < b < 1. Suppose also that investment is a linear function of the interest rate: I(r) = c - dr where c> 0 and d > 0. (a) Solve for Y as a function of r, the exogenous variables G and T, and the model's parameters a, b, c, and d.

This problem asks you to analyze the IS-LM model algebraically. Suppose consumption is a linear function of disposable income: C(YT) = a + b(Y − T) where a > 0 and 0 < b < 1. Suppose also that investment is a linear function of the interest rate: I(r) = c - dr where c> 0 and d > 0. (a) Solve for Y as a function of r, the exogenous variables G and T, and the model's parameters a, b, c, and d.

ENGR.ECONOMIC ANALYSIS

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Chapter1: Making Economics Decisions

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Question

This problem asks you to analyze the IS-LM model algebraically. Suppose consumption
is a linear function of disposable income:
C(YT) = a + b(YT)
where a > 0 and 0 < b < 1. Suppose also that investment is a linear function of the
interest rate:
I(r) = c — dr
where c> 0 and d > 0.
(a) Solve for Y as a function of r, the exogenous variables G and T, and the model's
parameters a, b, c, and d.
(b) How does the slope of the IS curve depend on the parameter d, the interest rate
sensitivity of investment? Refer to your answer to part (a), and explain the intu-
ition.
(c) Which will cause a bigger horizontal shift in the IS curve, a $100 tax cut or a $100
increase in government spending? Refer to your answer to part (a), and explain
the intuition.

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